The operation of an integrated circuit is often dependent on circuits designed to generate a reference signal (e.g., a reference voltage or a reference current). Because behaviors of devices implemented in silicon are susceptible to change with variations in, for example, characteristics of the silicon (i.e., “process” variations), power supply levels, and temperature, designers use circuits known in the art as “bandgap” circuits to generate a reference signal that has little or no dependence on process and power supply level variations and a well-defined dependence on temperature.
The use of at least one family of bandgap circuits to generate a temperature-stable reference signal (i.e., a reference that remains steady over an expected range of temperatures) relies on the properties of bipolar transistor technology. A bipolar transistor, of which there are two types (PNP and NPN), has three regions. The outer two regions are referred to as the “collector” and the “emitter,” and the middle region is referred to as the “base.” When implemented in silicon, the base-emitter junction voltage of a bipolar transistor is substantially constant (e.g., ˜0.7 volts) (such voltage referred to as the “on” voltage). This base-emitter junction voltage has a negative temperature coefficient, i.e., the voltage is complementary to absolute temperature (CTAT). Particularly, the voltage drop between the base and emitter decreases as temperature increases.
In typical bandgap circuits, a pair of bipolar transistors are operated at different current densities and are arranged to develop a voltage that is proportional to the difference in base-emitter junction voltages of the two transistors. This voltage difference has a positive temperature coefficient, i.e., the voltage is proportional to absolute temperature (PTAT). The PTAT voltage provided by the difference in base-emitter junction voltages of the two transistors is appropriately scaled and summed with the CTAT voltage of one of the transistors to produce the reference voltage/current.
FIG. 1 shows a circuit schematic of a typical bandgap circuit 10. In FIG. 1, a first bipolar transistor Q1 is “diode-connected” as its base and collector are both connected to ground. The emitter of transistor Q1 is connected to (i) an input of an operational amplifier 12 and (ii) a terminal of resistance R2. Another terminal of resistance R2 is connected to an output VREF of the operational amplifier 12. Also connected to the output VREF of the operational amplifier 12 is a terminal of resistance R3. Another terminal of resistance R3 is connected to (i) another input of the operational amplifier 12 and (ii) an emitter of a second bipolar transistor Q2 that is “diode-connected” as its base and collector are both connected to ground.
Accordingly, those skilled in the art will note that due to the feedback configuration of operational amplifier 12 in FIG. 1 described above, VREF may be given as:
                                          V            REF                    =                                    V              BEQ2                        +                                          (                                                      R                    2                                                        R                    1                                                  )                            ⁢                              V                T                            ⁢                              ln                ⁡                                  (                                                                                    R                        2                                            ⁢                                              A                        EQ1                                                                                                            R                        3                                            ⁢                                              A                        EQ2                                                                              )                                                                    ,                            (        1        )            where VBEQ2 represents the base-emitter junction voltage of transistor Q2, R1 represents the value of resistance R1, R2 represents the value of resistance R2, R3 represents the value of resistance R3, VT represents the threshold voltage, AEQ1 represents an area of transistor Q1, and AEQ2 represents an area of transistor Q2.
As shown above, those skilled in the art will note that an operational amplifier, such as the one shown in FIG. 1, performs, with electrical signals, mathematical operations such as addition, subtraction, multiplication, division, differentiation, integration, etc. The operational amplifier of a bandgap circuit may be implemented in silicon using transistors and/or capacitors that are deliberately enlarged to increase transconductance and compensate gain. Further, as power supply levels necessary for the proper operation of integrated circuits continue to decrease with advances in technology, designing and implementing an operational amplifier within such power supply level constraints may be difficult.